{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div align=\"right\"><i>Peter Norvig<br>March 2019</i></div>\n",
    "\n",
    "# Pairing Socks\n",
    "\n",
    "[Bram Cohen](https://en.wikipedia.org/wiki/Bram_Cohen) posed a problem that I'll restate thusly:\n",
    "\n",
    "> *You have N pairs of socks, all different, in the dryer. \n",
    "You pull random socks out one-by-one, placing each sock in one of C possible places on the countertop. \n",
    "If the latest sock pairs with another on the countertop, you put the pair away in a drawer. We can ask:*\n",
    "1. *What's the probability that you will pair up all 2N socks before you run out of the C places?*\n",
    "2. *For a given N, what is the minimum C to have a 50% chance?*\n",
    "3. *A 100% chance?*\n",
    "\n",
    "The third question is easy to solve analytically: to be 100% certain of pairing up N pairs, we would need N + 1 countertop spaces, because it is possible that the first N socks are all different, but the next one will always pair with one of the others.\n",
    "How about the other questions?\n",
    "- Can I come up with a mathematical formula? **No.**\n",
    "- Could I calculate an exact answer? **Only for small N.** Enumerating all permutations of socks would take *O*((2N)!), but since I don't care *which* sock is next, only whether it is a match/non-match, I could get that down to *O*(2<sup>(2N)</sup>), but that's still bad.\n",
    "- Could I do a simulation? **Yes.** And since we're mostly interested in events with probability around 50%, a simulation with, say, 1000 trials is likely to give very good approximations. If we were investigating events with probability 0.0001, we'd need many more trials.\n",
    "\n",
    "# Sock Pairing Simulation\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "from statistics import mean\n",
    "from functools import lru_cache"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pair_socks(C:int, socks:list) -> bool:\n",
    "    \"\"\"Can we pair up this sock ordering using a countertop of size C?\"\"\"\n",
    "    countertop = []\n",
    "    while socks and len(countertop) < C:\n",
    "        s = socks.pop()\n",
    "        countertop.remove(s) if s in countertop else countertop.append(s)\n",
    "    return not socks\n",
    "\n",
    "def random_socks(N):\n",
    "    \"\"\"A random ordering of N pairs of socks.\"\"\"\n",
    "    socks = 2 * list(range(N))\n",
    "    random.shuffle(socks)\n",
    "    return socks\n",
    "\n",
    "@lru_cache(None)\n",
    "def P(N, C, trials=1000) -> float: \n",
    "    \"\"\"Estimated probability of pairing up all N pairs on a countertop of size C.\"\"\"\n",
    "    return mean(pair_socks(C, random_socks(N)) for _ in range(trials))\n",
    "\n",
    "def minimum_C(N, p) -> int: \n",
    "    \"\"\"Minimum countertop size needed to have probability `p` of pairing up all socks.\"\"\"\n",
    "    return next(C for C in range(N // 2, 3*N) if P(N, C) > p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we can use `minimum_C` to find the countertop size necessary to give a 50% chance of pairing up all the socks, for various values of *N*. We see that the relation is very nearly linear, and the slope is a little more than 1/2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope = 0.52\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def fig(xlabel, ylabel):\n",
    "    \"\"\"Set up a figure.\"\"\"\n",
    "    plt.figure(figsize=(16,8)); plt.xlabel(xlabel); plt.ylabel(ylabel)\n",
    "    plt.minorticks_on()\n",
    "    plt.grid(b=True, which='major')\n",
    "    plt.grid(b=True, which='minor', alpha=0.2)\n",
    "    \n",
    "def plotC(Ns=range(10, 201, 10)):\n",
    "    fig('Number of pairs of socks', 'Size of countertop needed for > 50% paired up')\n",
    "    X = list(Ns)\n",
    "    Y = [minimum_C(N, 0.5) for N in Ns]\n",
    "    plt.plot(X, Y, 'o-')\n",
    "    plt.plot([X[0], X[-1]], [Y[0], Y[-1]])\n",
    "    print('Slope =', round(extent(Y) / extent(X), 2))\n",
    "    \n",
    "def extent(X): return max(X) - min(X)\n",
    "    \n",
    "plotC()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, for various numbers of pairs of socks ***N***, plot the probability `P(N, C)` of being able to pair up all the socks:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plotP(Ns=range(10, 101, 10)):\n",
    "    fig('Size of countertop, C', 'Probability of pairing up all socks, P(N, C)')\n",
    "    for N in Ns:\n",
    "        X = range(max(2, N // 2 - 8), min(N + 2, N // 2 + 18))\n",
    "        plt.plot(X, [P(N, C) for C in X], 'o-', label='N = {}'.format(N))\n",
    "    plt.legend()\n",
    "        \n",
    "plotP()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exact Probabilities\n",
    "\n",
    "I said that I could calculate the probability exactly for small values of ***N***. Let's do that. `Pexact` will call `pair_socks` once for each posssible permutation of the socks, and will use `fractions.Fraction` to get an exact rational number as the probability. This gives us a precise answer, and serves as a check on the inexact function `P`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from fractions import Fraction\n",
    "from itertools import permutations\n",
    "\n",
    "@lru_cache(None)\n",
    "def Pexact(N, C) -> float: \n",
    "    \"\"\"Exact probability of pairing up all N pairs on a countertop of size C.\"\"\"\n",
    "    return mean(Fraction(pair_socks(C, list(socks))) \n",
    "                for socks in permutations(list(range(N)) * 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'1000 trials': 0.487,\n",
       " '10,0000 trials': 0.464,\n",
       " 'exact': Fraction(7, 15),\n",
       " 'exact as decimal': 0.4666666666666667}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N, C = 5, 4\n",
    "{'1000 trials': P(N, C, trials=1000), \n",
    " '10,0000 trials': P(N, C, trials=10000), \n",
    " 'exact': Pexact(N, C),\n",
    " 'exact as decimal': float(Pexact(N, C))}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the `P` estimate with 1000 trials is not too bad, and with 10,000 trials it is much better."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
